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How to close gaps in mathematics?
Hello, I have been doing programming (web programming) for about 1.5 years now. I like programming and everything in general is going well, but I don’t want to be engaged in the web forever, but I want to do more serious programming with algorithms, etc., but there is one problem. At school, until the 7th grade, I did well, but then I “rolled down” and began to score on studies, etc., including mathematics, which, it seems to me, is not enough for me now, I sometimes feel like an inferior programmer (without normal knowledge of mathematics) , ready to devote time to studying mathematics, please advise me of any books on mathematics, but not those in which "dry formulas", but in which everything is explained in detail. I will be very grateful.
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How to close gaps in math and ?
If you failed from the 7th grade, then I recommend starting from the 7th grade - to tighten up the base, so to speak. So that later there would be no striving that something was missing in the database, so stop plugging to go further. Moreover, if there is still knowledge on the base, then things will go very very quickly, at the same time everything will be refreshed and systematized, the brains will warm up, on the eve of more complex university mathematics. I recommend starting with geometry, as it involves the brain in a more complex way, and it is believed (I was told so when I studied) that more than algebra develops the intellect). The easiest way is to download from the site of the publishing house "Prosveshchenie" an electronic supplement to the geometry textbook for grades 7-9 - this is an interactive training course, IMHO, of good quality, and start with it.
I will answer in the style of "many letters" in two calculations. The first is if you really want to master the world of math (but keep in mind that this will not help your career at all), the second is short and quick.
First:
If you want to go into algorithms, I would start with discrete mathematics. This area covers the basic needs very well (combinatorics, algorithms, logic).
There are many, many options for how to learn it, I can offer two options:
- The book "Discrete Mathematics and Combinatorics" by Anderson. This is simply an excellent theoretical base for immersing yourself in computer science. They start with logical proofs and statements, ending with number theory and information theory.
- On the stepic.org portal there was a course "Discrete Mathematics" that covered the base on the subject well, with a lot of emphasis on combinatorics and practical solutions.
In general, with such requests, you are in MOOC. On Coursera, Khan Academy, Udacity, you can find a lot of courses, both basic for complete beginners, and very strong and in-depth knowledge of both analytical combinatorics and discrete optimization.
Start with algorithms and the basics of mathematics: for example, the well-known course "Algorithms, Part I" starts on January 25, and then, as you progress, read additional literature in different areas. Sign up for SPOJ/Topcoder and dig deeper into the topics. From the basics: courses on mathematical statistics on Udacity, Linear Algebra on Khan Academy and Combinatorics on Coursera from MIPT.
Second:
But, in fact, computational methods, deep discrete mathematics, mathematical analysis or linear algebra will most likely not be useful to you, and in order to know basic algorithms and data structures, you need to know a little asymptotic analysis and probability theory. Therefore, these two universal books will help you achieve your goal extremely quickly:
- "Mathematics for Computer Science" - a book in the public domain from MIT teachers. The first link for such a request will most likely lead you to a PDF. 500 pages of concentrated knowledge that cover all the necessary knowledge for confident programming
- "Concrete Mathematics" - a desktop Bible for training the brain, solving problems and developing the mathematical apparatus of the programmer and algorithmic thinking.
By the way, I advise you to enroll in a course of algorithms and take it in both cases.
Good luck!
A school textbook that will give you what you need to close the gaps.
Here you can read www.bymath.net/studyguide/plan_rus.html
И да пребудет с тобою сила. ©
Программисту нужна не столько математика сколько алгоритмистика, это отдельная дисциплина. Кормен или Седжвик по главе на сон грядущий и Кнут как настольная библия. Там не так уж много сухих формул и просто здравого смысла обычно хватает.
Вся эта история про необходимость математики(выш. мата) в программировании - суть плод воображение тех кто максимально, от этого самого программирования, далек. Исключения есть, но это скорее частности.
И кроме того, если у тебя достаточно развито логическое мышление, и ты знаешь "что" ты хочешь сделать, о том "как", всегда можно загуглить.
www.mathprofi.ru спасает перед экзаменами в вузе уже второй год как, здесь принципе весь курс базовой математики, пройдешь это, и смело сможешь переходить на алгоритмы, которые уже перестанут казаться чем то сложным.
веб-программирование (да и вообще прикладное) и математика/наука вообще несвязные вещи. Ощущение неполноценности оправдано, вы просто обычный прикладной программист, тем более веб, ничего сложнее вызова методов уже имеющегося api или разметки страницы там не требуется.
Для начала, найдите методички по высшей математике местного ВУЗа/колледжа (естественно, не для гуманитарных специальностей). Их теории будет достаточно чтобы сформировать круг знаний и конкретизировать, что же не ясно. Постарайтесь также найти учебную программу, чтобы понять, что и в каком порядке нужно изучать - часто такие пособия "подвязаны" друг на друга очень сильно.
По алгоритмам в первую очередь возьмите "Алгоритмы. Руководство по разработке" С. Скиена. Там перечислены наиболее часто используемые алгоритмы, остальное вы сможете найти по ключевым словам из книги когда возникнет необходимость. И не подходите слишком академически к изучению всего, что написано в книге. Возможно, это никогда вам не пригодиться, нужно просто знать, что оно есть и как его найти.
Обращайте внимание в первую очередь на базу, которая потребуется практически везде - теория вероятностей, линейная алгебра, основы мат. анализа.
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